Computational Game Unit Balancing based on Game Theory

Abstract

Optimizing game elements through iterative human playtests can be time-consuming and insufficient for games with complex intransitive mechanics. Imbalances in games often require the release of numerous balance patches. We present a computational method for making each game unit equally preferable against a uniform play strategy. We leverage concepts from game theory to model intricate relationships among intransitive entities. Matching units against each other is modeled as a symmetric zero-sum game, where unit selection represents a strategy and the error is quantified using payoff values derived from unit parameters. The algorithm takes the initial unit parameters provided by the game designer and optimizes them with minimal changes using gradient descent. Consequently, the payoff matrix converges to a state where a uniform strategy is a near Nash equilibrium, ensuring that each unit is equally preferable under the optimized condition. We implemented a testing environment based on fictitious play and verified our results on different scenarios. While the majority of game theory research focuses on finding optimal strategies given specific environmental conditions, this paper takes a different perspective within the context of game design. We explore game theoretic concepts to address the goal of designing environments that lead to desired strategy choices.